You have an empty container, and an infinite number of marbles, each numbered with an integer from 1 to infinity.
At the start of the minute, you put marbles 1 - 10 into the container, then remove one of the marbles and throw it away. You do this again after 30 seconds, then again in 15 seconds, and again in 7.5 seconds. You continuosly repeat this process, each time after half as long an interval as the time before, until the minute is over.
Since this means that you repeated the process an infinite number of times, you have "processed" all your marbles.
How many marbles are in the container at the end of the minute if for every repetition (numbered N)
A. You remove the marble
numbered (10 * N)
B. You remove the marble numbered (N)
(In reply to
re(4): Respectfully, I disagree with all (save perhaps eric) by FatBoy)
OK, suppose you are correct. Then the final number of marbles you process is finite.
If it is finite, then there is a last marble you processed. What is the number on this marble? Call it M. It must have been processed in step M/10. But there was a step M/10+1 during which you processed marbles with numbers greater than M! So M can't have been the last marble processed.
The point is, there can't have been a "last" marble, since there are an infinite number of processing steps, and the set is in fact infinite.
There are an infinite number of integers. Theoretically, you CAN line them all up and count them. The only problem is that you have to do it infinitely fast, or else never stop.
In this problem, right up to the last infinitessimally small unit of time, you have hardly started. Almost all the marbles are processed at the very last instant, but in that last instant they are ALL, infinitely many of them, processed.
re(5): Respectfully, I disagree with all (save perhaps eric)
